Find the dimensions of the following vector spaces. (a) The vector space of 2 x 2 matrices with trace 0 (b) The vector space P3[x] of polynomials with degree less than 3 (c) The vector space of all diagonal 2 x 2 matrices

Find the dimensions of the following vector spaces. (a) The vector space of 2 x 2 matrices with trace 0 (b) The vector space P3[x] of polynomials with degree less than 3 (c) The vector space of all diagonal 2 x 2 matrices

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 55E: Identify the zero element and standard basis for each of the isomorphic vector spaces in Example 12....

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Question

Find the dimensions of the following vector spaces.
(a) The vector space of 2 x 2 matrices with trace 0
(b) The vector space P3[x] of polynomials with degree less than 3
(c) The vector space of all diagonal 2 x 2 matrices
(d) The vector space of all lower triangular 6 x 6 matrices
(e) The vector space RX
(1) The vector space R
4

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